.TH std::numeric_limits::tinyness_before 3 "2024.06.10" "http://cppreference.com" "C++ Standard Libary"
.SH NAME
std::numeric_limits::tinyness_before \- std::numeric_limits::tinyness_before

.SH Synopsis
   static const bool tinyness_before;      \fI(until C++11)\fP
   static constexpr bool tinyness_before;  \fI(since C++11)\fP

   The value of std::numeric_limits<T>::tinyness_before is true for all floating-point
   types T that test results of floating-point expressions for underflow before
   rounding.

.SH Standard specializations

   T                                value of std::numeric_limits<T>::tinyness_before
   /* non-specialized */            false
   bool                             false
   char                             false
   signed char                      false
   unsigned char                    false
   wchar_t                          false
   char8_t \fI(since C++20)\fP            false
   char16_t \fI(since C++11)\fP           false
   char32_t \fI(since C++11)\fP           false
   short                            false
   unsigned short                   false
   int                              false
   unsigned int                     false
   long                             false
   unsigned long                    false
   long long \fI(since C++11)\fP          false
   unsigned long long \fI(since C++11)\fP false
   float                            implementation-defined
   double                           implementation-defined
   long double                      implementation-defined

.SH Notes

   Standard-compliant IEEE 754 floating-point implementations are required to detect
   the floating-point underflow, and have two alternative situations where this can be
   done

    1. Underflow occurs (and FE_UNDERFLOW may be raised) if a computation produces a
       result whose absolute value, computed as though both the exponent range and the
       precision were unbounded, is smaller than std::numeric_limits<T>::min(). Such
       implementation detects tinyness before rounding (e.g. UltraSparc, POWER).
    2. Underflow occurs (and FE_UNDERFLOW may be raised) if after the rounding of the
       result to the target floating-point type (that is, rounding to
       std::numeric_limits<T>::digits bits), the result's absolute value is smaller
       than std::numeric_limits<T>::min(). Formally, the absolute value of a nonzero
       result computed as though the exponent range were unbounded is smaller than
       std::numeric_limits<T>::min(). Such implementation detects tinyness after
       rounding (e.g. SuperSparc).

.SH Example

   Multiplication of the largest subnormal number by the number one machine epsilon
   greater than 1.0 gives the tiny value 0x0.fffffffffffff8p-1022 before rounding, but
   normal value 1p-1022 after rounding. The implementation used to execute this test
   (IBM Power7) detects tinyness before rounding.


// Run this code

 #include <iostream>
 #include <limits>
 #include <cmath>
 #include <cfenv>

 int main()
 {
     std::cout << "Tinyness before: " << std::boolalpha
               << std::numeric_limits<double>::tinyness_before << '\\n';

     double denorm_max = std::nextafter(std::numeric_limits<double>::min(), 0);
     double multiplier = 1 + std::numeric_limits<double>::epsilon();

     std::feclearexcept(FE_ALL_EXCEPT);

     double result = denorm_max * multiplier; // Underflow only if tinyness_before

     if (std::fetestexcept(FE_UNDERFLOW))
         std::cout << "Underflow detected\\n";

     std::cout << std::hexfloat << denorm_max << " x " << multiplier  <<  " = "
               << result << '\\n';
 }

.SH Possible output:

 Tinyness before: true
 Underflow detected
 0xf.ffffffffffffp-1030 x 0x1.0000000000001p+0 = 0x1p-1022

.SH See also

   has_denorm_loss identifies the floating-point types that detect loss of precision as
   \fB[static]\fP        denormalization loss rather than inexact result
                   \fI(public static member constant)\fP
   has_denorm      identifies the denormalization style used by the floating-point type
   \fB[static]\fP        \fI(public static member constant)\fP
